Conductance peaks in open quantum dots

TL;DR

This paper introduces a simple method to analyze conductance fluctuations in open quantum dots by relating the density of maxima in conductance to the autocorrelation function, aiding in understanding parametric correlations.

Contribution

It extends the number of maxima method to open quantum dots, providing a practical way to measure conductance autocorrelation length without large data samples.

Findings

Average density of maxima is proportional to the inverse of the autocorrelation length.

The method is applicable for various external parameters like gate voltage and magnetic field.

It offers a straightforward approach to analyze conductance fluctuations in quantum dots.

Abstract

We present a simple measure of the conductance fluctuations in open ballistic chaotic quantum dots, extending the number of maxima method originally proposed for the statistical analysis of compound nuclear reactions. The average number of extreme points (maxima and minima) in the dimensionless conductance, $T$, as a function of an arbitrary external parameter $Z$, is directly related to the autocorrelation function of $T(Z)$. The parameter $Z$ can be associated to an applied gate voltage causing shape deformation in quantum dot, an external magnetic field, the Fermi energy, etc.. The average density of maxima is found to be $<\rho_{Z}> = \alpha_{Z}/Z_c$, where $\alpha_{Z}$ is a universal constant and $Z_c$ is the conductance autocorrelation length, which is system specific. The analysis of $<\rho_{Z}>$ does not require large statistic samples, providing a quite amenable way to access information about parametric correlations, such as $Z_c$.